Thermodynamics. AP Physics B

Transcription

1 Thermodynamics AP Physics B

2 Important Distinctions Thermodynamics study of processes in which energy is transferred as heat and work. There is a difference between heat and work: Heat is energy transferred due to a difference in temperature. Work is energy transferred that is unrelated to a difference in temperature. Open System where mass and energy are exchanged between objects and the environment. Closed System where mass does not enter or leave the system, but energy is exchanged with the environment. Isolated System closed system in which no energy is exchanged with the environment.

3 Work done by a gas Suppose you had a piston filled with a specific amount of gas. As you add heat, the temperature rises and thus the volume of the gas expands. The gas then applies a force on the piston wall pushing it a specific displacement. Thus it can be said that a gas can do WORK.

4 Work done by a gas Suppose you had a piston filled with a specific amount of gas. As you add heat, the temperature rises and thus the volume of the gas expands. The gas then applies a force on the piston wall pushing it a specific displacement. Thus it can be said that a gas can do WORK. where W is work done by the gas

5 Work is the AREA of a P vs. V graph by Here is how it would be written for W = work done on the gas: W = PΔV on ΔV = + = Work is done BY the gas (gas loses E) ΔV = = Work is done ON the gas (environment loses E) So the overall value of W on is (+) when work is done ON the gas.

6 Work is the AREA of a P vs. V graph Here is how it would be written for W = work done on the gas: W = PΔV on ΔV = + = Work is done BY the gas ΔV = = Work is done ON the gas W by = positive W on = negative When ΔV is positive, since energy is expelled BY the gas.

7 Work is the AREA of a P vs. V graph Here is how it would be written for W = work done on the gas: W = PΔV on ΔV = + = Work is done BY the gas ΔV = = Work is done ON the gas W by = positive W on = negative When ΔV is positive, since energy is expelled BY the gas. The negative sign in the equation for WORK is often misunderstood. Since work done BY a gas has a positive volume change we must understand that the gas itself is USING UP ENERGY or in other words, it is losing energy, thus the negative sign. When work is done ON a gas the change in volume is negative. This cancels out the negative sign in the equation. This makes sense, as some EXTERNAL agent is ADDING energy to the gas.

8 Internal Energy (ΔU) and Heat Energy (Q) All of the energy inside a system is called INTERNAL ENERGY, ΔU. When you add HEAT, (Q), you are adding energy and the internal energy INCREASES. Both are measured in Joules. But when you add heat, there is usually an increase in temperature associated with the change.

9 First Law of Thermodynamics The internal energy of a system tends to increase when HEAT is added and work is done ON the system. ΔU = Q +W ΔU = Q Add +W on or ΔU = Q Add W by The bottom line is that if you ADD heat and transfer work TO the gas, the internal energy must obviously go up, as you have MORE than what you started with.

10 Thermo in Chemistry Class vs. Physics Class In chemistry we look at the changes in chemical processes (like chemical reactions), but in physics we look at the changes in the physical processes. Physics reveals the underlying laws of thermodynamics, while chemistry likely applies the principles to particular chemical reactions under study. Chemical engineers (physicists) apply the laws of thermodynamics to large scale apparatuses that produce end products. Chemists focus on variables such as enthalpy (H) and Gibbs Free Energy (G), while physicists focus on variables such as heat supplied/removed (Q) and work done (W) by an expanding gas sample.

11 Difference between ΔH and Q Enthalpy is defined as H = U + PV or ΔH = ΔU + Δ(PV) ΔH = Q + W + Δ(PV) IF pressure is constant ΔH = Q + W + PΔV but since W = - PΔV, ΔH = Q But this is if and ONLY IF pressure is constant!

12 Another Difference Between ΔH and Q There is an important fundamental difference between enthalpy and heat. Lets say you are studying a process that takes your system from P 1, V 1 and T 1 to P 2, V 2 and T 2. Now, there are many different paths one can take between the two thermodynamic states. Along each of these paths, the values of Q and W will differ. However, no matter what path you take, ΔH for the transformation will always be the same because ΔH depends only on the initial and final states of the transformation. For example, an adiabatic path has Q = 0, whereas a nonadiabatic path between the same two states would have Q 0. State functions include: U, P, V, H, and S Non-state (path dependent) functions include: Q, W

13 Example Sketch a PV diagram and find the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 L to 3.0 L at a constant pressure of 3.0 atm. W BY = PΔV = ( ) = 600 J (b) The gas is then cooled at a constant volume until the pressure falls to 2.0 atm W = PΔV = 0,.since ΔV = 0

14 Example continued c) The gas is then compressed at a constant pressure of 2.0 atm from a volume of 3.0 L to 1.0 L. W ON = PΔV = ( ) = = -400 J d) The gas is then heated until its pressure increases from 2.0 atm to 3.0 atm at a constant volume.

15 Example continued What is the NET WORK? 600 J J = 200 J Rule of thumb: If the system rotates CW, the NET work by the gas is positive. NET work is the area inside the shape. If the system rotates CCW, the NET work done by the gas is negative (because work is done on the gas).

16 Example A series of thermodynamic processes is shown in the pv-diagram. In process ab 150 J of heat is added to the system, and in process bd, 600J of heat is added. Fill in the chart J 840 J 990 J J - _

17 Special Cases with the First Law Isothermal Process thermodynamic process in which the temperature of the system remains constant. Occurs often when heat reservoirs are present. Adiabatic Process thermodynamic process in which no heat is exchanged between the system and its environment. Occurs rapidly or when well insulated. Isobaric Process thermodynamic process in which the pressure of the system remains constant. Isochoric Process thermodynamic process in which the volume of the system remains constant. P P P P ΔT = 0; ΔU = 0, so W = -Q V Q = 0, so ΔU = W V W = -PΔV V ΔV = 0; W = 0, so ΔU = Q V

18 Thermodynamic Processes - Isothermal To keep the temperature constant both the pressure and volume change to compensate. (Volume goes up, pressure goes down) BOYLES LAW

19 Thermodynamic Processes - Isobaric Heat is added to the gas which increases the Internal Energy (U) Work is done by the gas as it changes in volume. The path of an isobaric process is a horizontal line called an isobar. U = Q - W can be used since the WORK is POSITIVE in this case

20 Thermodynamic Processes - Isovolumetric

21 Thermodynamic Processes - Adiabatic ADIABATIC- (GREEKadiabatos : "impassable") In other words, NO HEAT can leave or enter the system.

22 In Summary

23 Second Law of Thermodynamics Heat will not flow spontaneously from a colder body to a warmer body AND heat energy cannot be transformed completely into mechanical work. In other words: 1) Heat always flows from a hot body to a cold body 2) Nothing is 100% efficient

24 Engines Heat flows from a HOT reservoir to a COLD reservoir Q H = remove from, absorbs = hot Q C = exhausts to, expels = cold

25 Engine Efficiency In order to determine the thermal efficiency of an engine you have to look at how much ENERGY you get OUT based on how much you energy you take IN. In other words:

26 Is there an IDEAL engine model? Our goal is to figure out just how efficient such a heat engine can be: what s the most work we can possibly get for a given amount of fuel? The efficiency question was first posed and solved by Sadi Carnot in 1820, not long after steam engines had become efficient enough to begin replacing water wheels, at that time the main power sources for industry. Not surprisingly, perhaps, Carnot visualized the heat engine as a kind of water wheel in which heat (the fluid ) dropped from a high temperature to a low temperature, losing potential energy which the engine turned into work done, just like a water wheel.

27 Carnot Efficiency Carnot believed that there was an absolute zero of temperature, to which fluid would give up all its heat energy. Therefore, if it falls only half-way to absolute zero from its beginning temperature, it will give up half its heat, and an engine taking in heat at T and shedding it at ½T will be utilizing half the possible heat, and be 50% efficient. Picture a water wheel that takes in water at the top of a waterfall, but lets it out halfway down. So, the efficiency of an ideal engine operating between two temperatures will be equal to the fraction of the temperature drop towards absolute zero that the heat undergoes.

28 Carnot Efficiency Carnot temperatures must be expressed in KELVIN!!!!!! The Carnot model has 4 parts An Isothermal Expansion An Adiabatic Expansion An Isothermal Compression An Adiabatic Compression The PV diagram, in a way, shows us that the ratio of the heats are symbolic to the ratio of the 2 temperatures

29 Example A particular engine has a power output of 5000 W and an efficiency of 25%. If the engine expels 8000 J of heat in each cycle, find (a) the heat absorbed in each cycle and (b) the time for each cycle 10,667 J 2667 J 0.53 s

30 Example The efficiency of a Carnot engine is 30%. The engine absorbs 800 J of heat per cycle from a hot temperature reservoir at 500 K. Determine (a) the heat expelled per cycle and (b) the temperature of the cold reservoir 240 J 560 J 350 K